en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Functions >

extreme f(x)=(ln(2x))/x

Solution

extreme

Solution

Maximum (\frac{e}{2}, \frac{2}{e})

Solution steps

f^{'} (x) = \frac{1 - ln ( 2 x )}{x ^{2}}

Find intervals:

Increasing

: 0 < x < \frac{e}{2},

Decreasing

: \frac{e}{2} < x < \infty

Plug

x = \frac{e}{2}

into

\frac{ln ( 2 x )}{x} : \frac{2}{e}

Maximum (\frac{e}{2}, \frac{2}{e})

Graph

Popular Examples

extreme f(x)=(1+x)/(6-x)

extreme f(x)=-x^{2/3}(x-3)

extreme f(x)=-x^{2/3}(x-5)

extreme (x^2-7x+26)/(x-5)

extreme f(x)=3x^3e^{-x},-1<= x<= 5

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(ln(2x))/x ?
The extreme f(x)=(ln(2x))/x is Maximum(e/2 , 2/e)